Operational Risk Capital Allocation and Integration of Risks

this paper we present a risk capital framework which is based upon the assumption that for#h##ryy#hhtrq#bank market and credit risk management yield sufficient capital provision against these risks and give a threshold for the identification of the extreme losses being characterized as operational from the regulators' viewpoint. Our capital allocation rule links operational with market and credit risks and provides a risk measure for the tails of loss distributions at both the firm-wide and business unit levels. # 1

EMPIRICAL COPULAS FOR CDO TRANCHE PRICING USING RELATIVE ENTROPY

We discuss the general optimization problem of choosing a copula with minimum entropy relative to a specified copula and a computationally intensive procedure to solve its dual. These techniques are applied to constructing an empirical copula for CDO tranche pricing. The empirical copula is chosen to be as close as possible to the industry standard Gaussian copula while ensuring a close fit to market tranche quotes. We find that the empirical copula performs noticeably better than the base correlation approach in pricing non-standard tranches and that the market view of default dependence is influenced by maturity.Portfolio credit risk, CDO, copula, entropy, non-parametric estimation

A stochastic programming approach to managing liquid asset portfolios

summary:Maintaining liquid asset portfolios involves a high carry cost and is mandatory by law for most financial institutions. Taking this into account a financial institution's aim is to manage a liquid asset portfolio in an “optimal” way, such that it keeps the minimum required liquid assets to comply with regulations. In this paper we propose a multi-stage dynamic stochastic programming model for liquid asset portfolio management. The model allows for portfolio rebalancing decisions over a multi-period horizon, as well as for flexible risk management decisions, such as reinvesting coupons, at intermediate time steps. We show how our problem closely relates to insurance products with guarantees and utilize this in the formulation. We will discuss our formulation and implementation of a multi-stage stochastic programming model that minimizes the down-side risk of these portfolios. The model is back-tested on real market data over a period of two year